LMFDB - Embedded newform 983.2.a.b.1.38

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [983,2,Mod(1,983)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(983, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("983.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 983 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	983.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$7.84929451869$
Analytic rank:	$0$
Dimension:	$54$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.38
Character	$\chi$	$=$	983.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.38686 q^{2} -2.35222 q^{3} -0.0766077 q^{4} +4.36721 q^{5} -3.26221 q^{6} +2.06000 q^{7} -2.87997 q^{8} +2.53295 q^{9} +O(q^{10})$	\(q+1.38686 q^{2} -2.35222 q^{3} -0.0766077 q^{4} +4.36721 q^{5} -3.26221 q^{6} +2.06000 q^{7} -2.87997 q^{8} +2.53295 q^{9} +6.05673 q^{10} +4.93029 q^{11} +0.180198 q^{12} +2.75749 q^{13} +2.85694 q^{14} -10.2727 q^{15} -3.84092 q^{16} -7.18276 q^{17} +3.51286 q^{18} -4.62575 q^{19} -0.334562 q^{20} -4.84557 q^{21} +6.83764 q^{22} -0.187673 q^{23} +6.77434 q^{24} +14.0726 q^{25} +3.82427 q^{26} +1.09860 q^{27} -0.157812 q^{28} +4.97299 q^{29} -14.2468 q^{30} +0.945635 q^{31} +0.433117 q^{32} -11.5971 q^{33} -9.96152 q^{34} +8.99645 q^{35} -0.194044 q^{36} +7.05680 q^{37} -6.41529 q^{38} -6.48623 q^{39} -12.5775 q^{40} +10.5812 q^{41} -6.72015 q^{42} +5.31962 q^{43} -0.377698 q^{44} +11.0619 q^{45} -0.260277 q^{46} -3.66999 q^{47} +9.03469 q^{48} -2.75641 q^{49} +19.5167 q^{50} +16.8955 q^{51} -0.211245 q^{52} +2.22940 q^{53} +1.52362 q^{54} +21.5316 q^{55} -5.93274 q^{56} +10.8808 q^{57} +6.89686 q^{58} -11.6270 q^{59} +0.786965 q^{60} +7.51515 q^{61} +1.31147 q^{62} +5.21787 q^{63} +8.28251 q^{64} +12.0426 q^{65} -16.0837 q^{66} -0.993358 q^{67} +0.550255 q^{68} +0.441448 q^{69} +12.4769 q^{70} -14.3174 q^{71} -7.29483 q^{72} +2.45659 q^{73} +9.78683 q^{74} -33.1018 q^{75} +0.354368 q^{76} +10.1564 q^{77} -8.99552 q^{78} -11.3608 q^{79} -16.7741 q^{80} -10.1830 q^{81} +14.6747 q^{82} +8.83392 q^{83} +0.371208 q^{84} -31.3687 q^{85} +7.37759 q^{86} -11.6976 q^{87} -14.1991 q^{88} -13.7050 q^{89} +15.3414 q^{90} +5.68043 q^{91} +0.0143772 q^{92} -2.22434 q^{93} -5.08978 q^{94} -20.2016 q^{95} -1.01879 q^{96} -8.55417 q^{97} -3.82276 q^{98} +12.4882 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q + 8 q^{2} + 6 q^{3} + 64 q^{4} + 7 q^{5} + 5 q^{6} + 31 q^{7} + 24 q^{8} + 74 q^{9}+O(q^{10}) $ 54 * q + 8 * q^2 + 6 * q^3 + 64 * q^4 + 7 * q^5 + 5 * q^6 + 31 * q^7 + 24 * q^8 + 74 * q^9	\( 54 q + 8 q^{2} + 6 q^{3} + 64 q^{4} + 7 q^{5} + 5 q^{6} + 31 q^{7} + 24 q^{8} + 74 q^{9} + 15 q^{10} + 8 q^{11} + 10 q^{12} + 34 q^{13} + q^{14} + 3 q^{15} + 80 q^{16} + 32 q^{17} + 28 q^{18} + 15 q^{19} + 4 q^{20} + 11 q^{21} + 25 q^{22} + 15 q^{23} - 7 q^{24} + 125 q^{25} - 14 q^{26} + 12 q^{27} + 78 q^{28} + 8 q^{29} - 32 q^{30} + 16 q^{31} + 36 q^{32} + 38 q^{33} - 8 q^{34} - 2 q^{35} + 65 q^{36} + 80 q^{37} - 14 q^{38} + 16 q^{39} + 36 q^{40} + 30 q^{41} - 10 q^{42} + 53 q^{43} + 6 q^{44} + 3 q^{45} + 24 q^{46} + 22 q^{47} + 7 q^{48} + 111 q^{49} + 14 q^{50} - 10 q^{51} + 45 q^{52} + 10 q^{53} - 8 q^{54} + 12 q^{55} - 30 q^{56} + 106 q^{57} + 61 q^{58} - 4 q^{59} - 61 q^{60} + 24 q^{61} - 12 q^{62} + 73 q^{63} + 86 q^{64} + 32 q^{65} - 43 q^{66} + 54 q^{67} + 33 q^{68} - 30 q^{69} - 21 q^{70} - 6 q^{71} + 60 q^{72} + 172 q^{73} - 32 q^{74} - 36 q^{75} + 7 q^{76} - 12 q^{77} - 3 q^{78} + 28 q^{79} - 66 q^{80} + 86 q^{81} + 4 q^{82} + 14 q^{83} - 58 q^{84} + 99 q^{85} - 31 q^{86} - 27 q^{87} + 5 q^{88} - 5 q^{89} - 45 q^{90} - 11 q^{91} + 20 q^{92} + 27 q^{93} - 39 q^{94} + 5 q^{95} - 87 q^{96} + 127 q^{97} - 29 q^{98} - 21 q^{99}+O(q^{100}) \) 54 * q + 8 * q^2 + 6 * q^3 + 64 * q^4 + 7 * q^5 + 5 * q^6 + 31 * q^7 + 24 * q^8 + 74 * q^9 + 15 * q^10 + 8 * q^11 + 10 * q^12 + 34 * q^13 + q^14 + 3 * q^15 + 80 * q^16 + 32 * q^17 + 28 * q^18 + 15 * q^19 + 4 * q^20 + 11 * q^21 + 25 * q^22 + 15 * q^23 - 7 * q^24 + 125 * q^25 - 14 * q^26 + 12 * q^27 + 78 * q^28 + 8 * q^29 - 32 * q^30 + 16 * q^31 + 36 * q^32 + 38 * q^33 - 8 * q^34 - 2 * q^35 + 65 * q^36 + 80 * q^37 - 14 * q^38 + 16 * q^39 + 36 * q^40 + 30 * q^41 - 10 * q^42 + 53 * q^43 + 6 * q^44 + 3 * q^45 + 24 * q^46 + 22 * q^47 + 7 * q^48 + 111 * q^49 + 14 * q^50 - 10 * q^51 + 45 * q^52 + 10 * q^53 - 8 * q^54 + 12 * q^55 - 30 * q^56 + 106 * q^57 + 61 * q^58 - 4 * q^59 - 61 * q^60 + 24 * q^61 - 12 * q^62 + 73 * q^63 + 86 * q^64 + 32 * q^65 - 43 * q^66 + 54 * q^67 + 33 * q^68 - 30 * q^69 - 21 * q^70 - 6 * q^71 + 60 * q^72 + 172 * q^73 - 32 * q^74 - 36 * q^75 + 7 * q^76 - 12 * q^77 - 3 * q^78 + 28 * q^79 - 66 * q^80 + 86 * q^81 + 4 * q^82 + 14 * q^83 - 58 * q^84 + 99 * q^85 - 31 * q^86 - 27 * q^87 + 5 * q^88 - 5 * q^89 - 45 * q^90 - 11 * q^91 + 20 * q^92 + 27 * q^93 - 39 * q^94 + 5 * q^95 - 87 * q^96 + 127 * q^97 - 29 * q^98 - 21 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.38686	0.980661	0.490331	−	0.871537i	$-0.336876\pi$
$2$	1.38686	0.980661	0.490331	+	0.871537i	$0.336876\pi$
$3$	−2.35222	−1.35806	−0.679028	−	0.734112i	$-0.737599\pi$
$3$	−2.35222	−1.35806	−0.679028	+	0.734112i	$0.737599\pi$
$4$	−0.0766077	−0.0383039
$5$	4.36721	1.95308	0.976539	−	0.215342i	$-0.0690865\pi$
$5$	4.36721	1.95308	0.976539	+	0.215342i	$0.0690865\pi$
$6$	−3.26221	−1.33179
$7$	2.06000	0.778606	0.389303	−	0.921110i	$-0.372716\pi$
$7$	2.06000	0.778606	0.389303	+	0.921110i	$0.372716\pi$
$8$	−2.87997	−1.01822
$9$	2.53295	0.844317
$10$	6.05673	1.91531
$11$	4.93029	1.48654	0.743269	−	0.668993i	$-0.233274\pi$
$11$	4.93029	1.48654	0.743269	+	0.668993i	$0.233274\pi$
$12$	0.180198	0.0520188
$13$	2.75749	0.764791	0.382395	−	0.923999i	$-0.375099\pi$
$13$	2.75749	0.764791	0.382395	+	0.923999i	$0.375099\pi$
$14$	2.85694	0.763549
$15$	−10.2727	−2.65239
$16$	−3.84092	−0.960229
$17$	−7.18276	−1.74208	−0.871038	−	0.491215i	$-0.836553\pi$
$17$	−7.18276	−1.74208	−0.871038	+	0.491215i	$0.836553\pi$
$18$	3.51286	0.827989
$19$	−4.62575	−1.06122	−0.530610	−	0.847616i	$-0.678037\pi$
$19$	−4.62575	−1.06122	−0.530610	+	0.847616i	$0.678037\pi$
$20$	−0.334562	−0.0748104
$21$	−4.84557	−1.05739
$22$	6.83764	1.45779
$23$	−0.187673	−0.0391325	−0.0195662	−	0.999809i	$-0.506229\pi$
$23$	−0.187673	−0.0391325	−0.0195662	+	0.999809i	$0.506229\pi$
$24$	6.77434	1.38281
$25$	14.0726	2.81451
$26$	3.82427	0.750000
$27$	1.09860	0.211427
$28$	−0.157812	−0.0298236
$29$	4.97299	0.923460	0.461730	−	0.887020i	$-0.347229\pi$
$29$	4.97299	0.923460	0.461730	+	0.887020i	$0.347229\pi$
$30$	−14.2468	−2.60109
$31$	0.945635	0.169841	0.0849205	−	0.996388i	$-0.472936\pi$
$31$	0.945635	0.169841	0.0849205	+	0.996388i	$0.472936\pi$
$32$	0.433117	0.0765650
$33$	−11.5971	−2.01880
$34$	−9.96152	−1.70839
$35$	8.99645	1.52068
$36$	−0.194044	−0.0323406
$37$	7.05680	1.16013	0.580066	−	0.814570i	$-0.303027\pi$
$37$	7.05680	1.16013	0.580066	+	0.814570i	$0.303027\pi$
$38$	−6.41529	−1.04070
$39$	−6.48623	−1.03863
$40$	−12.5775	−1.98867
$41$	10.5812	1.65251	0.826255	−	0.563296i	$-0.190467\pi$
$41$	10.5812	1.65251	0.826255	+	0.563296i	$0.190467\pi$
$42$	−6.72015	−1.03694
$43$	5.31962	0.811234	0.405617	−	0.914043i	$-0.367057\pi$
$43$	5.31962	0.811234	0.405617	+	0.914043i	$0.367057\pi$
$44$	−0.377698	−0.0569401
$45$	11.0619	1.64902
$46$	−0.260277	−0.0383757
$47$	−3.66999	−0.535323	−0.267662	−	0.963513i	$-0.586251\pi$
$47$	−3.66999	−0.535323	−0.267662	+	0.963513i	$0.586251\pi$
$48$	9.03469	1.30404
$49$	−2.75641	−0.393772
$50$	19.5167	2.76008
$51$	16.8955	2.36584
$52$	−0.211245	−0.0292944
$53$	2.22940	0.306231	0.153116	−	0.988208i	$-0.451069\pi$
$53$	2.22940	0.306231	0.153116	+	0.988208i	$0.451069\pi$
$54$	1.52362	0.207338
$55$	21.5316	2.90332
$56$	−5.93274	−0.792796
$57$	10.8808	1.44120
$58$	6.89686	0.905601
$59$	−11.6270	−1.51371	−0.756854	−	0.653584i	$-0.773265\pi$
$59$	−11.6270	−1.51371	−0.756854	+	0.653584i	$0.773265\pi$
$60$	0.786965	0.101597
$61$	7.51515	0.962217	0.481108	−	0.876661i	$-0.340234\pi$
$61$	7.51515	0.962217	0.481108	+	0.876661i	$0.340234\pi$
$62$	1.31147	0.166556
$63$	5.21787	0.657390
$64$	8.28251	1.03531
$65$	12.0426	1.49370
$66$	−16.0837	−1.97976
$67$	−0.993358	−0.121358	−0.0606790	−	0.998157i	$-0.519327\pi$
$67$	−0.993358	−0.121358	−0.0606790	+	0.998157i	$0.519327\pi$
$68$	0.550255	0.0667282
$69$	0.441448	0.0531441
$70$	12.4769	1.49127
$71$	−14.3174	−1.69917	−0.849583	−	0.527456i	$-0.823146\pi$
$71$	−14.3174	−1.69917	−0.849583	+	0.527456i	$0.823146\pi$
$72$	−7.29483	−0.859704
$73$	2.45659	0.287523	0.143761	−	0.989612i	$-0.454080\pi$
$73$	2.45659	0.287523	0.143761	+	0.989612i	$0.454080\pi$
$74$	9.78683	1.13770
$75$	−33.1018	−3.82227
$76$	0.354368	0.0406488
$77$	10.1564	1.15743
$78$	−8.99552	−1.01854
$79$	−11.3608	−1.27819	−0.639097	−	0.769126i	$-0.720692\pi$
$79$	−11.3608	−1.27819	−0.639097	+	0.769126i	$0.720692\pi$
$80$	−16.7741	−1.87540
$81$	−10.1830	−1.13145
$82$	14.6747	1.62055
$83$	8.83392	0.969649	0.484824	−	0.874612i	$-0.338884\pi$
$83$	8.83392	0.969649	0.484824	+	0.874612i	$0.338884\pi$
$84$	0.371208	0.0405022
$85$	−31.3687	−3.40241
$86$	7.37759	0.795546
$87$	−11.6976	−1.25411
$88$	−14.1991	−1.51363
$89$	−13.7050	−1.45273	−0.726366	−	0.687308i	$-0.758792\pi$
$89$	−13.7050	−1.45273	−0.726366	+	0.687308i	$0.758792\pi$
$90$	15.3414	1.61713
$91$	5.68043	0.595471
$92$	0.0143772	0.00149893
$93$	−2.22434	−0.230654
$94$	−5.08978	−0.524971
$95$	−20.2016	−2.07265
$96$	−1.01879	−0.103980
$97$	−8.55417	−0.868544	−0.434272	−	0.900782i	$-0.642994\pi$
$97$	−8.55417	−0.868544	−0.434272	+	0.900782i	$0.642994\pi$
$98$	−3.82276	−0.386157
$99$	12.4882	1.25511
$100$	−1.07807	−0.107807
$101$	15.4430	1.53663	0.768317	−	0.640070i	$-0.221095\pi$
$101$	15.4430	1.53663	0.768317	+	0.640070i	$0.221095\pi$
$102$	23.4317	2.32008
$103$	9.39198	0.925420	0.462710	−	0.886510i	$-0.346877\pi$
$103$	9.39198	0.925420	0.462710	+	0.886510i	$0.346877\pi$
$104$	−7.94150	−0.778728
$105$	−21.1617	−2.06517
$106$	3.09187	0.300309
$107$	9.33940	0.902874	0.451437	−	0.892303i	$-0.350912\pi$
$107$	9.33940	0.902874	0.451437	+	0.892303i	$0.350912\pi$
$108$	−0.0841616	−0.00809845
$109$	−6.66966	−0.638838	−0.319419	−	0.947614i	$-0.603488\pi$
$109$	−6.66966	−0.638838	−0.319419	+	0.947614i	$0.603488\pi$
$110$	29.8614	2.84718
$111$	−16.5992	−1.57552
$112$	−7.91228	−0.747640
$113$	11.0732	1.04168	0.520841	−	0.853654i	$-0.325619\pi$
$113$	11.0732	1.04168	0.520841	+	0.853654i	$0.325619\pi$
$114$	15.0902	1.41333
$115$	−0.819608	−0.0764288
$116$	−0.380969	−0.0353721
$117$	6.98459	0.645725
$118$	−16.1251	−1.48443
$119$	−14.7965	−1.35639
$120$	29.5850	2.70073
$121$	13.3077	1.20979
$122$	10.4225	0.943608
$123$	−24.8894	−2.24420
$124$	−0.0724429	−0.00650557
$125$	39.6218	3.54388
$126$	7.23648	0.644677
$127$	−14.2252	−1.26228	−0.631140	−	0.775669i	$-0.717413\pi$
$127$	−14.2252	−1.26228	−0.631140	+	0.775669i	$0.717413\pi$
$128$	10.6205	0.938726
$129$	−12.5129	−1.10170
$130$	16.7014	1.46481
$131$	−3.97575	−0.347363	−0.173682	−	0.984802i	$-0.555566\pi$
$131$	−3.97575	−0.347363	−0.173682	+	0.984802i	$0.555566\pi$
$132$	0.888430	0.0773279
$133$	−9.52904	−0.826273
$134$	−1.37765	−0.119011
$135$	4.79784	0.412932
$136$	20.6862	1.77382
$137$	−5.63917	−0.481787	−0.240894	−	0.970552i	$-0.577440\pi$
$137$	−5.63917	−0.481787	−0.240894	+	0.970552i	$0.577440\pi$
$138$	0.612229	0.0521164
$139$	−22.2422	−1.88656	−0.943281	−	0.331995i	$-0.892278\pi$
$139$	−22.2422	−1.88656	−0.943281	+	0.331995i	$0.892278\pi$
$140$	−0.689198	−0.0582478
$141$	8.63263	0.726999
$142$	−19.8563	−1.66631
$143$	13.5952	1.13689
$144$	−9.72885	−0.810737
$145$	21.7181	1.80359
$146$	3.40696	0.281962
$147$	6.48368	0.534765
$148$	−0.540606	−0.0444375
$149$	−5.00485	−0.410014	−0.205007	−	0.978761i	$-0.565722\pi$
$149$	−5.00485	−0.410014	−0.205007	+	0.978761i	$0.565722\pi$
$150$	−45.9077	−3.74835
$151$	−9.21530	−0.749930	−0.374965	−	0.927039i	$-0.622345\pi$
$151$	−9.21530	−0.749930	−0.374965	+	0.927039i	$0.622345\pi$
$152$	13.3220	1.08056
$153$	−18.1936	−1.47086
$154$	14.0855	1.13504
$155$	4.12979	0.331713
$156$	0.496895	0.0397835
$157$	−9.58280	−0.764791	−0.382396	−	0.923999i	$-0.624901\pi$
$157$	−9.58280	−0.764791	−0.382396	+	0.923999i	$0.624901\pi$
$158$	−15.7559	−1.25348
$159$	−5.24403	−0.415879
$160$	1.89152	0.149537
$161$	−0.386606	−0.0304688
$162$	−14.1225	−1.10956
$163$	8.22714	0.644399	0.322200	−	0.946672i	$-0.395578\pi$
$163$	8.22714	0.644399	0.322200	+	0.946672i	$0.395578\pi$
$164$	−0.810604	−0.0632975
$165$	−50.6472	−3.94288
$166$	12.2514	0.950897
$167$	−9.22331	−0.713721	−0.356860	−	0.934158i	$-0.616153\pi$
$167$	−9.22331	−0.713721	−0.356860	+	0.934158i	$0.616153\pi$
$168$	13.9551	1.07666
$169$	−5.39624	−0.415095
$170$	−43.5041	−3.33661
$171$	−11.7168	−0.896006
$172$	−0.407524	−0.0310734
$173$	−13.0111	−0.989213	−0.494606	−	0.869117i	$-0.664688\pi$
$173$	−13.0111	−0.989213	−0.494606	+	0.869117i	$0.664688\pi$
$174$	−16.2229	−1.22986
$175$	28.9894	2.19140
$176$	−18.9368	−1.42742
$177$	27.3493	2.05570
$178$	−19.0070	−1.42464
$179$	19.0909	1.42692	0.713461	−	0.700695i	$-0.247126\pi$
$179$	19.0909	1.42692	0.713461	+	0.700695i	$0.247126\pi$
$180$	−0.847430	−0.0631637
$181$	0.725039	0.0538917	0.0269459	−	0.999637i	$-0.491422\pi$
$181$	0.725039	0.0538917	0.0269459	+	0.999637i	$0.491422\pi$
$182$	7.87798	0.583955
$183$	−17.6773	−1.30674
$184$	0.540493	0.0398457
$185$	30.8186	2.26583
$186$	−3.08486	−0.226193
$187$	−35.4131	−2.58966
$188$	0.281150	0.0205049
$189$	2.26312	0.164618
$190$	−28.0169	−2.03256
$191$	12.1211	0.877049	0.438525	−	0.898719i	$-0.355501\pi$
$191$	12.1211	0.877049	0.438525	+	0.898719i	$0.355501\pi$
$192$	−19.4823	−1.40601
$193$	5.98188	0.430585	0.215292	−	0.976550i	$-0.430930\pi$
$193$	5.98188	0.430585	0.215292	+	0.976550i	$0.430930\pi$
$194$	−11.8635	−0.851747
$195$	−28.3268	−2.02852
$196$	0.211162	0.0150830
$197$	−1.01464	−0.0722904	−0.0361452	−	0.999347i	$-0.511508\pi$
$197$	−1.01464	−0.0722904	−0.0361452	+	0.999347i	$0.511508\pi$
$198$	17.3194	1.23084
$199$	12.5707	0.891116	0.445558	−	0.895253i	$-0.353005\pi$
$199$	12.5707	0.891116	0.445558	+	0.895253i	$0.353005\pi$
$200$	−40.5286	−2.86580
$201$	2.33660	0.164811
$202$	21.4173	1.50692
$203$	10.2443	0.719012
$204$	−1.29432	−0.0906207
$205$	46.2105	3.22748
$206$	13.0254	0.907523
$207$	−0.475366	−0.0330402
$208$	−10.5913	−0.734374
$209$	−22.8063	−1.57754
$210$	−29.3483	−2.02523
$211$	−0.638811	−0.0439776	−0.0219888	−	0.999758i	$-0.507000\pi$
$211$	−0.638811	−0.0439776	−0.0219888	+	0.999758i	$0.507000\pi$
$212$	−0.170789	−0.0117298
$213$	33.6778	2.30756
$214$	12.9525	0.885413
$215$	23.2319	1.58440
$216$	−3.16395	−0.215280
$217$	1.94801	0.132239
$218$	−9.24991	−0.626483
$219$	−5.77845	−0.390472
$220$	−1.64949	−0.111208
$221$	−19.8064	−1.33232
$222$	−23.0208	−1.54505
$223$	−18.6078	−1.24607	−0.623035	−	0.782194i	$-0.714101\pi$
$223$	−18.6078	−1.24607	−0.623035	+	0.782194i	$0.714101\pi$
$224$	0.892221	0.0596140
$225$	35.6451	2.37634
$226$	15.3571	1.02154
$227$	−18.7424	−1.24398	−0.621988	−	0.783027i	$-0.713675\pi$
$227$	−18.7424	−1.24398	−0.621988	+	0.783027i	$0.713675\pi$
$228$	−0.833553	−0.0552034
$229$	−16.7769	−1.10865	−0.554323	−	0.832301i	$-0.687023\pi$
$229$	−16.7769	−1.10865	−0.554323	+	0.832301i	$0.687023\pi$
$230$	−1.13668	−0.0749507
$231$	−23.8901	−1.57185
$232$	−14.3221	−0.940289
$233$	−15.0694	−0.987229	−0.493615	−	0.869681i	$-0.664325\pi$
$233$	−15.0694	−0.987229	−0.493615	+	0.869681i	$0.664325\pi$
$234$	9.68668	0.633238
$235$	−16.0276	−1.04553
$236$	0.890719	0.0579809
$237$	26.7232	1.73586
$238$	−20.5207	−1.33016
$239$	−8.35505	−0.540443	−0.270222	−	0.962798i	$-0.587097\pi$
$239$	−8.35505	−0.540443	−0.270222	+	0.962798i	$0.587097\pi$
$240$	39.4564	2.54690
$241$	−14.2291	−0.916578	−0.458289	−	0.888803i	$-0.651537\pi$
$241$	−14.2291	−0.916578	−0.458289	+	0.888803i	$0.651537\pi$
$242$	18.4560	1.18640
$243$	20.6569	1.32514
$244$	−0.575719	−0.0368566
$245$	−12.0378	−0.769068
$246$	−34.5182	−2.20080
$247$	−12.7555	−0.811611
$248$	−2.72340	−0.172936
$249$	−20.7793	−1.31684
$250$	54.9501	3.47535
$251$	−4.29177	−0.270894	−0.135447	−	0.990785i	$-0.543247\pi$
$251$	−4.29177	−0.270894	−0.135447	+	0.990785i	$0.543247\pi$
$252$	−0.399729	−0.0251806
$253$	−0.925281	−0.0581719
$254$	−19.7284	−1.23787
$255$	73.7861	4.62066
$256$	−1.83585	−0.114741
$257$	16.6694	1.03981	0.519903	−	0.854225i	$-0.325968\pi$
$257$	16.6694	1.03981	0.519903	+	0.854225i	$0.325968\pi$
$258$	−17.3537	−1.08040
$259$	14.5370	0.903285
$260$	−0.922553	−0.0572143
$261$	12.5963	0.779693
$262$	−5.51383	−0.340645
$263$	−22.3180	−1.37618	−0.688092	−	0.725624i	$-0.741551\pi$
$263$	−22.3180	−1.37618	−0.688092	+	0.725624i	$0.741551\pi$
$264$	33.3994	2.05559
$265$	9.73625	0.598093
$266$	−13.2155	−0.810293
$267$	32.2373	1.97289
$268$	0.0760989	0.00464848
$269$	−17.6900	−1.07858	−0.539289	−	0.842121i	$-0.681307\pi$
$269$	−17.6900	−1.07858	−0.539289	+	0.842121i	$0.681307\pi$
$270$	6.65395	0.404947
$271$	11.3371	0.688682	0.344341	−	0.938845i	$-0.388102\pi$
$271$	11.3371	0.688682	0.344341	+	0.938845i	$0.388102\pi$
$272$	27.5884	1.67279
$273$	−13.3616	−0.808683
$274$	−7.82077	−0.472470
$275$	69.3818	4.18388
$276$	−0.0338183	−0.00203563
$277$	13.2700	0.797315	0.398657	−	0.917100i	$-0.369476\pi$
$277$	13.2700	0.797315	0.398657	+	0.917100i	$0.369476\pi$
$278$	−30.8470	−1.85008
$279$	2.39525	0.143400
$280$	−25.9095	−1.54839
$281$	−26.2000	−1.56296	−0.781481	−	0.623929i	$-0.785536\pi$
$281$	−26.2000	−1.56296	−0.781481	+	0.623929i	$0.785536\pi$
$282$	11.9723	0.712940
$283$	−18.4919	−1.09923	−0.549613	−	0.835419i	$-0.685225\pi$
$283$	−18.4919	−1.09923	−0.549613	+	0.835419i	$0.685225\pi$
$284$	1.09682	0.0650846
$285$	47.5188	2.81477
$286$	18.8547	1.11490
$287$	21.7973	1.28665
$288$	1.09706	0.0646451
$289$	34.5921	2.03483
$290$	30.1200	1.76871
$291$	20.1213	1.17953
$292$	−0.188194	−0.0110132
$293$	17.0458	0.995823	0.497912	−	0.867228i	$-0.334100\pi$
$293$	17.0458	0.995823	0.497912	+	0.867228i	$0.334100\pi$
$294$	8.99199	0.524423
$295$	−50.7777	−2.95639
$296$	−20.3234	−1.18127
$297$	5.41644	0.314294
$298$	−6.94105	−0.402084
$299$	−0.517506	−0.0299282
$300$	2.53585	0.146408
$301$	10.9584	0.631632
$302$	−12.7804	−0.735428
$303$	−36.3253	−2.08683
$304$	17.7671	1.01901
$305$	32.8203	1.87928
$306$	−25.2320	−1.44242
$307$	−0.203033	−0.0115877	−0.00579384	−	0.999983i	$-0.501844\pi$
$307$	−0.203033	−0.0115877	−0.00579384	+	0.999983i	$0.501844\pi$
$308$	−0.778057	−0.0443339
$309$	−22.0920	−1.25677
$310$	5.72746	0.325298
$311$	−22.2256	−1.26030	−0.630150	−	0.776473i	$-0.717007\pi$
$311$	−22.2256	−1.26030	−0.630150	+	0.776473i	$0.717007\pi$
$312$	18.6802	1.05756
$313$	5.28324	0.298627	0.149313	−	0.988790i	$-0.452294\pi$
$313$	5.28324	0.298627	0.149313	+	0.988790i	$0.452294\pi$
$314$	−13.2900	−0.750001
$315$	22.7876	1.28393
$316$	0.870328	0.0489598
$317$	8.29382	0.465827	0.232914	−	0.972497i	$-0.425174\pi$
$317$	8.29382	0.465827	0.232914	+	0.972497i	$0.425174\pi$
$318$	−7.27276	−0.407836
$319$	24.5183	1.37276
$320$	36.1715	2.02205
$321$	−21.9684	−1.22615
$322$	−0.536170	−0.0298796
$323$	33.2257	1.84873
$324$	0.780097	0.0433387
$325$	38.8050	2.15251
$326$	11.4099	0.631937
$327$	15.6885	0.867577
$328$	−30.4737	−1.68263
$329$	−7.56017	−0.416806
$330$	−70.2407	−3.86663
$331$	−19.3249	−1.06219	−0.531097	−	0.847311i	$-0.678220\pi$
$331$	−19.3249	−1.06219	−0.531097	+	0.847311i	$0.678220\pi$
$332$	−0.676746	−0.0371413
$333$	17.8745	0.979518
$334$	−12.7915	−0.699918
$335$	−4.33821	−0.237022
$336$	18.6114	1.01534
$337$	−13.9351	−0.759093	−0.379546	−	0.925173i	$-0.623920\pi$
$337$	−13.9351	−0.759093	−0.379546	+	0.925173i	$0.623920\pi$
$338$	−7.48385	−0.407068
$339$	−26.0467	−1.41466
$340$	2.40308	0.130325
$341$	4.66225	0.252475
$342$	−16.2496	−0.878678
$343$	−20.0982	−1.08520
$344$	−15.3204	−0.826019
$345$	1.92790	0.103795
$346$	−18.0446	−0.970082
$347$	4.21929	0.226503	0.113252	−	0.993566i	$-0.463873\pi$
$347$	4.21929	0.226503	0.113252	+	0.993566i	$0.463873\pi$
$348$	0.896124	0.0480373
$349$	−4.28169	−0.229193	−0.114597	−	0.993412i	$-0.536558\pi$
$349$	−4.28169	−0.229193	−0.114597	+	0.993412i	$0.536558\pi$
$350$	40.2044	2.14902
$351$	3.02939	0.161697
$352$	2.13539	0.113817
$353$	2.27158	0.120904	0.0604521	−	0.998171i	$-0.480746\pi$
$353$	2.27158	0.120904	0.0604521	+	0.998171i	$0.480746\pi$
$354$	37.9298	2.01595
$355$	−62.5272	−3.31860
$356$	1.04991	0.0556452
$357$	34.8046	1.84206
$358$	26.4765	1.39933
$359$	13.5770	0.716566	0.358283	−	0.933613i	$-0.383362\pi$
$359$	13.5770	0.716566	0.358283	+	0.933613i	$0.383362\pi$
$360$	−31.8581	−1.67907
$361$	2.39758	0.126188
$362$	1.00553	0.0528495
$363$	−31.3028	−1.64297
$364$	−0.435165	−0.0228088
$365$	10.7285	0.561554
$366$	−24.5160	−1.28147
$367$	11.5180	0.601236	0.300618	−	0.953745i	$-0.402807\pi$
$367$	11.5180	0.601236	0.300618	+	0.953745i	$0.402807\pi$
$368$	0.720836	0.0375762
$369$	26.8017	1.39524
$370$	42.7412	2.22201
$371$	4.59255	0.238433
$372$	0.170402	0.00883492
$373$	14.7022	0.761253	0.380626	−	0.924729i	$-0.375708\pi$
$373$	14.7022	0.761253	0.380626	+	0.924729i	$0.375708\pi$
$374$	−49.1132	−2.53958
$375$	−93.1993	−4.81279
$376$	10.5695	0.545079
$377$	13.7130	0.706254
$378$	3.13864	0.161434
$379$	11.5750	0.594569	0.297285	−	0.954789i	$-0.403919\pi$
$379$	11.5750	0.594569	0.297285	+	0.954789i	$0.403919\pi$
$380$	1.54760	0.0793903
$381$	33.4608	1.71425
$382$	16.8103	0.860088
$383$	−2.18710	−0.111756	−0.0558779	−	0.998438i	$-0.517796\pi$
$383$	−2.18710	−0.111756	−0.0558779	+	0.998438i	$0.517796\pi$
$384$	−24.9817	−1.27484
$385$	44.3551	2.26055
$386$	8.29605	0.422258
$387$	13.4743	0.684939
$388$	0.655315	0.0332686
$389$	30.8175	1.56251	0.781255	−	0.624212i	$-0.214580\pi$
$389$	30.8175	1.56251	0.781255	+	0.624212i	$0.214580\pi$
$390$	−39.2854	−1.98929
$391$	1.34801	0.0681718
$392$	7.93838	0.400949
$393$	9.35185	0.471739
$394$	−1.40717	−0.0708923
$395$	−49.6152	−2.49641
$396$	−0.956691	−0.0480755
$397$	6.94326	0.348472	0.174236	−	0.984704i	$-0.444254\pi$
$397$	6.94326	0.348472	0.174236	+	0.984704i	$0.444254\pi$
$398$	17.4339	0.873883
$399$	22.4144	1.12212
$400$	−54.0515	−2.70258
$401$	−27.1302	−1.35482	−0.677409	−	0.735606i	$-0.736897\pi$
$401$	−27.1302	−1.35482	−0.677409	+	0.735606i	$0.736897\pi$
$402$	3.24055	0.161624
$403$	2.60758	0.129893
$404$	−1.18305	−0.0588590
$405$	−44.4714	−2.20980
$406$	14.2075	0.705107
$407$	34.7921	1.72458
$408$	−48.6585	−2.40895
$409$	24.9049	1.23147	0.615734	−	0.787954i	$-0.288860\pi$
$409$	24.9049	1.23147	0.615734	+	0.787954i	$0.288860\pi$
$410$	64.0877	3.16507
$411$	13.2646	0.654294
$412$	−0.719498	−0.0354471
$413$	−23.9516	−1.17858
$414$	−0.659268	−0.0324013
$415$	38.5796	1.89380
$416$	1.19432	0.0585562
$417$	52.3187	2.56206
$418$	−31.6292	−1.54704
$419$	−31.7599	−1.55157	−0.775787	−	0.630994i	$-0.782647\pi$
$419$	−31.7599	−1.55157	−0.775787	+	0.630994i	$0.782647\pi$
$420$	1.62115	0.0791038
$421$	34.2987	1.67162	0.835808	−	0.549021i	$-0.184999\pi$
$421$	34.2987	1.67162	0.835808	+	0.549021i	$0.184999\pi$
$422$	−0.885944	−0.0431271
$423$	−9.29590	−0.451982
$424$	−6.42060	−0.311812
$425$	−101.080	−4.90309
$426$	46.7065	2.26294
$427$	15.4812	0.749188
$428$	−0.715470	−0.0345836
$429$	−31.9790	−1.54396
$430$	32.2195	1.55376
$431$	2.54116	0.122404	0.0612018	−	0.998125i	$-0.480507\pi$
$431$	2.54116	0.122404	0.0612018	+	0.998125i	$0.480507\pi$
$432$	−4.21965	−0.203018
$433$	13.6624	0.656574	0.328287	−	0.944578i	$-0.393529\pi$
$433$	13.6624	0.656574	0.328287	+	0.944578i	$0.393529\pi$
$434$	2.70162	0.129682
$435$	−51.0858	−2.44938
$436$	0.510947	0.0244699
$437$	0.868128	0.0415282
$438$	−8.01393	−0.382920
$439$	8.93229	0.426315	0.213158	−	0.977018i	$-0.431625\pi$
$439$	8.93229	0.426315	0.213158	+	0.977018i	$0.431625\pi$
$440$	−62.0105	−2.95623
$441$	−6.98184	−0.332469
$442$	−27.4688	−1.30656
$443$	1.83838	0.0873441	0.0436720	−	0.999046i	$-0.486094\pi$
$443$	1.83838	0.0873441	0.0436720	+	0.999046i	$0.486094\pi$
$444$	1.27162	0.0603486
$445$	−59.8529	−2.83730
$446$	−25.8065	−1.22197
$447$	11.7725	0.556822
$448$	17.0619	0.806101
$449$	−35.7057	−1.68506	−0.842528	−	0.538653i	$-0.818933\pi$
$449$	−35.7057	−1.68506	−0.842528	+	0.538653i	$0.818933\pi$
$450$	49.4349	2.33038
$451$	52.1685	2.45652
$452$	−0.848294	−0.0399004
$453$	21.6764	1.01845
$454$	−25.9931	−1.21992
$455$	24.8076	1.16300
$456$	−31.3364	−1.46746
$457$	21.8578	1.02247	0.511233	−	0.859442i	$-0.329189\pi$
$457$	21.8578	1.02247	0.511233	+	0.859442i	$0.329189\pi$
$458$	−23.2672	−1.08721
$459$	−7.89102	−0.368321
$460$	0.0627883	0.00292752
$461$	−8.33482	−0.388191	−0.194096	−	0.980983i	$-0.562177\pi$
$461$	−8.33482	−0.388191	−0.194096	+	0.980983i	$0.562177\pi$
$462$	−33.1323	−1.54145
$463$	−6.00043	−0.278863	−0.139432	−	0.990232i	$-0.544528\pi$
$463$	−6.00043	−0.278863	−0.139432	+	0.990232i	$0.544528\pi$
$464$	−19.1008	−0.886733
$465$	−9.71418	−0.450484
$466$	−20.8992	−0.968137
$467$	21.4391	0.992081	0.496041	−	0.868299i	$-0.334787\pi$
$467$	21.4391	0.992081	0.496041	+	0.868299i	$0.334787\pi$
$468$	−0.535073	−0.0247338
$469$	−2.04632	−0.0944901
$470$	−22.2282	−1.02531
$471$	22.5409	1.03863
$472$	33.4855	1.54129
$473$	26.2273	1.20593
$474$	37.0615	1.70229
$475$	−65.0962	−2.98682
$476$	1.13352	0.0519550
$477$	5.64695	0.258556
$478$	−11.5873	−0.529991
$479$	−1.23652	−0.0564980	−0.0282490	−	0.999601i	$-0.508993\pi$
$479$	−1.23652	−0.0564980	−0.0282490	+	0.999601i	$0.508993\pi$
$480$	−4.44926	−0.203080
$481$	19.4591	0.887257
$482$	−19.7338	−0.898852
$483$	0.909383	0.0413783
$484$	−1.01948	−0.0463398
$485$	−37.3579	−1.69633
$486$	28.6483	1.29951
$487$	16.2009	0.734132	0.367066	−	0.930195i	$-0.380362\pi$
$487$	16.2009	0.734132	0.367066	+	0.930195i	$0.380362\pi$
$488$	−21.6434	−0.979752
$489$	−19.3521	−0.875130
$490$	−16.6948	−0.754195
$491$	2.43523	0.109900	0.0549501	−	0.998489i	$-0.482500\pi$
$491$	2.43523	0.109900	0.0549501	+	0.998489i	$0.482500\pi$
$492$	1.90672	0.0859616
$493$	−35.7198	−1.60874
$494$	−17.6901	−0.795915
$495$	54.5385	2.45133
$496$	−3.63210	−0.163086
$497$	−29.4939	−1.32298
$498$	−28.8181	−1.29137
$499$	20.6667	0.925169	0.462585	−	0.886575i	$-0.346922\pi$
$499$	20.6667	0.925169	0.462585	+	0.886575i	$0.346922\pi$
$500$	−3.03534	−0.135744
$501$	21.6953	0.969273
$502$	−5.95210	−0.265655
$503$	1.79445	0.0800107	0.0400053	−	0.999199i	$-0.487263\pi$
$503$	1.79445	0.0800107	0.0400053	+	0.999199i	$0.487263\pi$
$504$	−15.0273	−0.669371
$505$	67.4428	3.00116
$506$	−1.28324	−0.0570470
$507$	12.6932	0.563723
$508$	1.08976	0.0483502
$509$	−28.6768	−1.27108	−0.635539	−	0.772069i	$-0.719222\pi$
$509$	−28.6768	−1.27108	−0.635539	+	0.772069i	$0.719222\pi$
$510$	102.331	4.53131
$511$	5.06058	0.223867
$512$	−23.7870	−1.05125
$513$	−5.08187	−0.224370
$514$	23.1182	1.01970
$515$	41.0168	1.80742
$516$	0.958587	0.0421994
$517$	−18.0941	−0.795778
$518$	20.1608	0.885817
$519$	30.6049	1.34341
$520$	−34.6822	−1.52092
$521$	−3.21373	−0.140796	−0.0703980	−	0.997519i	$-0.522427\pi$
$521$	−3.21373	−0.140796	−0.0703980	+	0.997519i	$0.522427\pi$
$522$	17.4694	0.764615
$523$	5.23757	0.229023	0.114511	−	0.993422i	$-0.463470\pi$
$523$	5.23757	0.229023	0.114511	+	0.993422i	$0.463470\pi$
$524$	0.304573	0.0133053
$525$	−68.1896	−2.97604
$526$	−30.9520	−1.34957
$527$	−6.79227	−0.295876
$528$	44.5436	1.93851
$529$	−22.9648	−0.998469
$530$	13.5029	0.586527
$531$	−29.4506	−1.27805
$532$	0.729998	0.0316494
$533$	29.1777	1.26382
$534$	44.7088	1.93474
$535$	40.7872	1.76338
$536$	2.86084	0.123570
$537$	−44.9061	−1.93784
$538$	−24.5336	−1.05772
$539$	−13.5899	−0.585358
$540$	−0.367552	−0.0158169
$541$	27.9328	1.20093	0.600463	−	0.799653i	$-0.294983\pi$
$541$	27.9328	1.20093	0.600463	+	0.799653i	$0.294983\pi$
$542$	15.7231	0.675364
$543$	−1.70545	−0.0731880
$544$	−3.11098	−0.133382
$545$	−29.1278	−1.24770
$546$	−18.5308	−0.793043
$547$	−25.2194	−1.07830	−0.539151	−	0.842209i	$-0.681255\pi$
$547$	−25.2194	−1.07830	−0.539151	+	0.842209i	$0.681255\pi$
$548$	0.432004	0.0184543
$549$	19.0355	0.812416
$550$	96.2231	4.10297
$551$	−23.0038	−0.979995
$552$	−1.27136	−0.0541126
$553$	−23.4033	−0.995210
$554$	18.4036	0.781896
$555$	−72.4921	−3.07712
$556$	1.70393	0.0722626
$557$	14.0320	0.594554	0.297277	−	0.954791i	$-0.403922\pi$
$557$	14.0320	0.594554	0.297277	+	0.954791i	$0.403922\pi$
$558$	3.32188	0.140626
$559$	14.6688	0.620424
$560$	−34.5546	−1.46020
$561$	83.2995	3.51691
$562$	−36.3359	−1.53274
$563$	−39.3434	−1.65813	−0.829063	−	0.559156i	$-0.811125\pi$
$563$	−39.3434	−1.65813	−0.829063	+	0.559156i	$0.811125\pi$
$564$	−0.661326	−0.0278469
$565$	48.3591	2.03448
$566$	−25.6457	−1.07797
$567$	−20.9770	−0.880951
$568$	41.2338	1.73013
$569$	−2.14448	−0.0899014	−0.0449507	−	0.998989i	$-0.514313\pi$
$569$	−2.14448	−0.0899014	−0.0449507	+	0.998989i	$0.514313\pi$
$570$	65.9021	2.76033
$571$	−29.0110	−1.21407	−0.607036	−	0.794674i	$-0.707642\pi$
$571$	−29.0110	−1.21407	−0.607036	+	0.794674i	$0.707642\pi$
$572$	−1.04150	−0.0435473
$573$	−28.5114	−1.19108
$574$	30.2299	1.26177
$575$	−2.64104	−0.110139
$576$	20.9792	0.874132
$577$	−13.7155	−0.570983	−0.285491	−	0.958381i	$-0.592157\pi$
$577$	−13.7155	−0.570983	−0.285491	+	0.958381i	$0.592157\pi$
$578$	47.9746	1.99548
$579$	−14.0707	−0.584758
$580$	−1.66377	−0.0690844
$581$	18.1979	0.754974
$582$	27.9055	1.15672
$583$	10.9916	0.455224
$584$	−7.07492	−0.292762
$585$	30.5032	1.26115
$586$	23.6401	0.976565
$587$	−3.92034	−0.161810	−0.0809050	−	0.996722i	$-0.525781\pi$
$587$	−3.92034	−0.161810	−0.0809050	+	0.996722i	$0.525781\pi$
$588$	−0.496700	−0.0204836
$589$	−4.37427	−0.180239
$590$	−70.4217	−2.89922
$591$	2.38667	0.0981744
$592$	−27.1046	−1.11399
$593$	20.4808	0.841047	0.420523	−	0.907282i	$-0.361846\pi$
$593$	20.4808	0.841047	0.420523	+	0.907282i	$0.361846\pi$
$594$	7.51186	0.308215
$595$	−64.6194	−2.64914
$596$	0.383410	0.0157051
$597$	−29.5692	−1.21019
$598$	−0.717711	−0.0293494
$599$	31.8894	1.30297	0.651483	−	0.758664i	$-0.274147\pi$
$599$	31.8894	1.30297	0.651483	+	0.758664i	$0.274147\pi$
$600$	95.3323	3.89192
$601$	8.69833	0.354812	0.177406	−	0.984138i	$-0.443229\pi$
$601$	8.69833	0.354812	0.177406	+	0.984138i	$0.443229\pi$
$602$	15.1978	0.619417
$603$	−2.51613	−0.102465
$604$	0.705963	0.0287252
$605$	58.1178	2.36282
$606$	−50.3783	−2.04648
$607$	41.0548	1.66636	0.833182	−	0.552998i	$-0.186516\pi$
$607$	41.0548	1.66636	0.833182	+	0.552998i	$0.186516\pi$
$608$	−2.00349	−0.0812523
$609$	−24.0970	−0.976458
$610$	45.5173	1.84294
$611$	−10.1200	−0.409410
$612$	1.39377	0.0563398
$613$	16.2143	0.654887	0.327444	−	0.944871i	$-0.393813\pi$
$613$	16.2143	0.654887	0.327444	+	0.944871i	$0.393813\pi$
$614$	−0.281579	−0.0113636
$615$	−108.697	−4.38310
$616$	−29.2501	−1.17852
$617$	14.8540	0.597999	0.298999	−	0.954253i	$-0.403347\pi$
$617$	14.8540	0.597999	0.298999	+	0.954253i	$0.403347\pi$
$618$	−30.6387	−1.23247
$619$	22.0928	0.887986	0.443993	−	0.896030i	$-0.353561\pi$
$619$	22.0928	0.887986	0.443993	+	0.896030i	$0.353561\pi$
$620$	−0.316374	−0.0127059
$621$	−0.206178	−0.00827365
$622$	−30.8240	−1.23593
$623$	−28.2324	−1.13111
$624$	24.9131	0.997321
$625$	102.674	4.10697
$626$	7.32714	0.292851
$627$	53.6455	2.14239
$628$	0.734117	0.0292944
$629$	−50.6874	−2.02104
$630$	31.6033	1.25910
$631$	22.9975	0.915516	0.457758	−	0.889077i	$-0.348653\pi$
$631$	22.9975	0.915516	0.457758	+	0.889077i	$0.348653\pi$
$632$	32.7189	1.30149
$633$	1.50263	0.0597240
$634$	11.5024	0.456819
$635$	−62.1243	−2.46533
$636$	0.401734	0.0159298
$637$	−7.60077	−0.301153
$638$	34.0035	1.34621
$639$	−36.2653	−1.43463
$640$	46.3819	1.83341
$641$	−26.1878	−1.03435	−0.517177	−	0.855878i	$-0.673017\pi$
$641$	−26.1878	−1.03435	−0.517177	+	0.855878i	$0.673017\pi$
$642$	−30.4671	−1.20244
$643$	2.92117	0.115200	0.0575998	−	0.998340i	$-0.481655\pi$
$643$	2.92117	0.115200	0.0575998	+	0.998340i	$0.481655\pi$
$644$	0.0296170	0.00116707
$645$	−54.6466	−2.15171
$646$	46.0795	1.81297
$647$	−17.8183	−0.700511	−0.350256	−	0.936654i	$-0.613905\pi$
$647$	−17.8183	−0.700511	−0.350256	+	0.936654i	$0.613905\pi$
$648$	29.3268	1.15207
$649$	−57.3245	−2.25018
$650$	53.8172	2.11088
$651$	−4.58214	−0.179588
$652$	−0.630262	−0.0246830
$653$	22.4785	0.879653	0.439827	−	0.898083i	$-0.355040\pi$
$653$	22.4785	0.879653	0.439827	+	0.898083i	$0.355040\pi$
$654$	21.7579	0.850799
$655$	−17.3630	−0.678427
$656$	−40.6416	−1.58679
$657$	6.22243	0.242760
$658$	−10.4849	−0.408745
$659$	26.4787	1.03147	0.515733	−	0.856750i	$-0.327520\pi$
$659$	26.4787	1.03147	0.515733	+	0.856750i	$0.327520\pi$
$660$	3.87996	0.151027
$661$	−47.8846	−1.86250	−0.931248	−	0.364385i	$-0.881279\pi$
$661$	−47.8846	−1.86250	−0.931248	+	0.364385i	$0.881279\pi$
$662$	−26.8011	−1.04165
$663$	46.5891	1.80937
$664$	−25.4414	−0.987320
$665$	−41.6154	−1.61377
$666$	24.7896	0.960576
$667$	−0.933294	−0.0361373
$668$	0.706576	0.0273383
$669$	43.7697	1.69223
$670$	−6.01650	−0.232438
$671$	37.0519	1.43037
$672$	−2.09870	−0.0809592
$673$	−13.6522	−0.526253	−0.263127	−	0.964761i	$-0.584754\pi$
$673$	−13.6522	−0.526253	−0.263127	+	0.964761i	$0.584754\pi$
$674$	−19.3261	−0.744413
$675$	15.4602	0.595062
$676$	0.413394	0.0158998
$677$	−23.2765	−0.894587	−0.447294	−	0.894387i	$-0.647612\pi$
$677$	−23.2765	−0.894587	−0.447294	+	0.894387i	$0.647612\pi$
$678$	−36.1232	−1.38730
$679$	−17.6216	−0.676254
$680$	90.3409	3.46442
$681$	44.0862	1.68939
$682$	6.46591	0.247592
$683$	−30.5885	−1.17044	−0.585218	−	0.810876i	$-0.698991\pi$
$683$	−30.5885	−1.17044	−0.585218	+	0.810876i	$0.698991\pi$
$684$	0.897597	0.0343205
$685$	−24.6275	−0.940968
$686$	−27.8734	−1.06421
$687$	39.4629	1.50560
$688$	−20.4322	−0.778971
$689$	6.14754	0.234203
$690$	2.67373	0.101787
$691$	−1.19286	−0.0453786	−0.0226893	−	0.999743i	$-0.507223\pi$
$691$	−1.19286	−0.0453786	−0.0226893	+	0.999743i	$0.507223\pi$
$692$	0.996748	0.0378907
$693$	25.7256	0.977235
$694$	5.85158	0.222123
$695$	−97.1366	−3.68460
$696$	33.6887	1.27697
$697$	−76.0025	−2.87880
$698$	−5.93812	−0.224761
$699$	35.4466	1.34071
$700$	−2.22082	−0.0839389
$701$	17.0811	0.645146	0.322573	−	0.946545i	$-0.395452\pi$
$701$	17.0811	0.645146	0.322573	+	0.946545i	$0.395452\pi$
$702$	4.20136	0.158570
$703$	−32.6430	−1.23115
$704$	40.8351	1.53903
$705$	37.7006	1.41989
$706$	3.15038	0.118566
$707$	31.8125	1.19643
$708$	−2.09517	−0.0787413
$709$	42.4691	1.59496	0.797480	−	0.603345i	$-0.206166\pi$
$709$	42.4691	1.59496	0.797480	+	0.603345i	$0.206166\pi$
$710$	−86.7168	−3.25442
$711$	−28.7764	−1.07920
$712$	39.4702	1.47921
$713$	−0.177470	−0.00664630
$714$	48.2693	1.80643
$715$	59.3733	2.22043
$716$	−1.46251	−0.0546566
$717$	19.6529	0.733952
$718$	18.8294	0.702708
$719$	32.1726	1.19984	0.599919	−	0.800061i	$-0.295200\pi$
$719$	32.1726	1.19984	0.599919	+	0.800061i	$0.295200\pi$
$720$	−42.4880	−1.58343
$721$	19.3475	0.720537
$722$	3.32511	0.123748
$723$	33.4700	1.24476
$724$	−0.0555436	−0.00206426
$725$	69.9826	2.59909
$726$	−43.4127	−1.61120
$727$	11.9462	0.443058	0.221529	−	0.975154i	$-0.428895\pi$
$727$	11.9462	0.443058	0.221529	+	0.975154i	$0.428895\pi$
$728$	−16.3595	−0.606323
$729$	−18.0406	−0.668170
$730$	14.8789	0.550694
$731$	−38.2096	−1.41323
$732$	1.35422	0.0500534
$733$	37.9220	1.40068	0.700341	−	0.713809i	$-0.253031\pi$
$733$	37.9220	1.40068	0.700341	+	0.713809i	$0.253031\pi$
$734$	15.9739	0.589608
$735$	28.3156	1.04444
$736$	−0.0812843	−0.00299618
$737$	−4.89754	−0.180403
$738$	37.1704	1.36826
$739$	27.9521	1.02823	0.514117	−	0.857720i	$-0.328120\pi$
$739$	27.9521	1.02823	0.514117	+	0.857720i	$0.328120\pi$
$740$	−2.36094	−0.0867899
$741$	30.0037	1.10221
$742$	6.36924	0.233822
$743$	42.9058	1.57406	0.787030	−	0.616915i	$-0.211618\pi$
$743$	42.9058	1.57406	0.787030	+	0.616915i	$0.211618\pi$
$744$	6.40605	0.234857
$745$	−21.8573	−0.800788
$746$	20.3900	0.746531
$747$	22.3759	0.818691
$748$	2.71292	0.0991941
$749$	19.2392	0.702983
$750$	−129.255	−4.71972
$751$	15.1345	0.552264	0.276132	−	0.961120i	$-0.410947\pi$
$751$	15.1345	0.552264	0.276132	+	0.961120i	$0.410947\pi$
$752$	14.0961	0.514033
$753$	10.0952	0.367890
$754$	19.0180	0.692595
$755$	−40.2452	−1.46467
$756$	−0.173373	−0.00630550
$757$	−16.6286	−0.604377	−0.302188	−	0.953248i	$-0.597717\pi$
$757$	−16.6286	−0.604377	−0.302188	+	0.953248i	$0.597717\pi$
$758$	16.0530	0.583071
$759$	2.17647	0.0790008
$760$	58.1802	2.11042
$761$	−13.2172	−0.479125	−0.239562	−	0.970881i	$-0.577004\pi$
$761$	−13.2172	−0.479125	−0.239562	+	0.970881i	$0.577004\pi$
$762$	46.4055	1.68109
$763$	−13.7395	−0.497403
$764$	−0.928567	−0.0335944
$765$	−79.4553	−2.87271
$766$	−3.03321	−0.109595
$767$	−32.0614	−1.15767
$768$	4.31834	0.155824
$769$	−10.5499	−0.380440	−0.190220	−	0.981741i	$-0.560920\pi$
$769$	−10.5499	−0.380440	−0.190220	+	0.981741i	$0.560920\pi$
$770$	61.5145	2.21683
$771$	−39.2101	−1.41212
$772$	−0.458258	−0.0164931
$773$	−27.7888	−0.999494	−0.499747	−	0.866171i	$-0.666574\pi$
$773$	−27.7888	−0.999494	−0.499747	+	0.866171i	$0.666574\pi$
$774$	18.6871	0.671693
$775$	13.3075	0.478020
$776$	24.6358	0.884373
$777$	−34.1943	−1.22671
$778$	42.7397	1.53229
$779$	−48.9461	−1.75368
$780$	2.17005	0.0777002
$781$	−70.5890	−2.52587
$782$	1.86951	0.0668534
$783$	5.46334	0.195244
$784$	10.5871	0.378112
$785$	−41.8502	−1.49370
$786$	12.9698	0.462616
$787$	−21.9046	−0.780815	−0.390407	−	0.920642i	$-0.627666\pi$
$787$	−21.9046	−0.780815	−0.390407	+	0.920642i	$0.627666\pi$
$788$	0.0777295	0.00276900
$789$	52.4968	1.86894
$790$	−68.8096	−2.44813
$791$	22.8108	0.811059
$792$	−35.9656	−1.27798
$793$	20.7230	0.735894
$794$	9.62937	0.341733
$795$	−22.9018	−0.812244
$796$	−0.963015	−0.0341332
$797$	−8.89220	−0.314978	−0.157489	−	0.987521i	$-0.550340\pi$
$797$	−8.89220	−0.314978	−0.157489	+	0.987521i	$0.550340\pi$
$798$	31.0858	1.10042
$799$	26.3607	0.932574
$800$	6.09507	0.215493
$801$	−34.7142	−1.22657
$802$	−37.6259	−1.32862
$803$	12.1117	0.427413
$804$	−0.179002	−0.00631290
$805$	−1.68839	−0.0595079
$806$	3.61636	0.127381
$807$	41.6108	1.46477
$808$	−44.4753	−1.56464
$809$	−30.7671	−1.08171	−0.540857	−	0.841115i	$-0.681900\pi$
$809$	−30.7671	−1.08171	−0.540857	+	0.841115i	$0.681900\pi$
$810$	−61.6758	−2.16707
$811$	−6.73481	−0.236491	−0.118246	−	0.992984i	$-0.537727\pi$
$811$	−6.73481	−0.236491	−0.118246	+	0.992984i	$0.537727\pi$
$812$	−0.784795	−0.0275409
$813$	−26.6675	−0.935269
$814$	48.2519	1.69123
$815$	35.9297	1.25856
$816$	−64.8940	−2.27175
$817$	−24.6072	−0.860898
$818$	34.5397	1.20765
$819$	14.3882	0.502766
$820$	−3.54008	−0.123625
$821$	−35.8996	−1.25290	−0.626452	−	0.779460i	$-0.715494\pi$
$821$	−35.8996	−1.25290	−0.626452	+	0.779460i	$0.715494\pi$
$822$	18.3962	0.641641
$823$	−19.1091	−0.666102	−0.333051	−	0.942909i	$-0.608078\pi$
$823$	−19.1091	−0.666102	−0.333051	+	0.942909i	$0.608078\pi$
$824$	−27.0487	−0.942285
$825$	−163.201	−5.68194
$826$	−33.2176	−1.15579
$827$	32.0276	1.11371	0.556854	−	0.830610i	$-0.312008\pi$
$827$	32.0276	1.11371	0.556854	+	0.830610i	$0.312008\pi$
$828$	0.0364167	0.00126557
$829$	−33.1389	−1.15096	−0.575481	−	0.817815i	$-0.695185\pi$
$829$	−33.1389	−1.15096	−0.575481	+	0.817815i	$0.695185\pi$
$830$	53.5047	1.85717
$831$	−31.2139	−1.08280
$832$	22.8389	0.791798
$833$	19.7986	0.685982
$834$	72.5589	2.51251
$835$	−40.2802	−1.39395
$836$	1.74714	0.0604260
$837$	1.03888	0.0359089
$838$	−44.0467	−1.52157
$839$	41.5262	1.43364	0.716822	−	0.697256i	$-0.245596\pi$
$839$	41.5262	1.43364	0.716822	+	0.697256i	$0.245596\pi$
$840$	60.9450	2.10280
$841$	−4.26942	−0.147221
$842$	47.5676	1.63929
$843$	61.6283	2.12259
$844$	0.0489379	0.00168451
$845$	−23.5665	−0.810714
$846$	−12.8922	−0.443241
$847$	27.4139	0.941954
$848$	−8.56292	−0.294052
$849$	43.4970	1.49281
$850$	−140.184	−4.80827
$851$	−1.32437	−0.0453988
$852$	−2.57998	−0.0883885
$853$	−24.4264	−0.836343	−0.418171	−	0.908368i	$-0.637329\pi$
$853$	−24.4264	−0.836343	−0.418171	+	0.908368i	$0.637329\pi$
$854$	21.4703	0.734699
$855$	−51.1698	−1.74997
$856$	−26.8972	−0.919328
$857$	−31.1747	−1.06491	−0.532453	−	0.846460i	$-0.678730\pi$
$857$	−31.1747	−1.06491	−0.532453	+	0.846460i	$0.678730\pi$
$858$	−44.3505	−1.51410
$859$	−23.9376	−0.816740	−0.408370	−	0.912817i	$-0.633903\pi$
$859$	−23.9376	−0.816740	−0.408370	+	0.912817i	$0.633903\pi$
$860$	−1.77974	−0.0606888
$861$	−51.2721	−1.74735
$862$	3.52425	0.120036
$863$	32.1060	1.09290	0.546451	−	0.837491i	$-0.315979\pi$
$863$	32.1060	1.09290	0.546451	+	0.837491i	$0.315979\pi$
$864$	0.475824	0.0161879
$865$	−56.8221	−1.93201
$866$	18.9479	0.643877
$867$	−81.3683	−2.76341
$868$	−0.149232	−0.00506527
$869$	−56.0122	−1.90008
$870$	−70.8490	−2.40201
$871$	−2.73918	−0.0928134
$872$	19.2084	0.650480
$873$	−21.6673	−0.733326
$874$	1.20398	0.0407251
$875$	81.6209	2.75929
$876$	0.442674	0.0149566
$877$	34.9072	1.17873	0.589366	−	0.807866i	$-0.299378\pi$
$877$	34.9072	1.17873	0.589366	+	0.807866i	$0.299378\pi$
$878$	12.3879	0.418071
$879$	−40.0954	−1.35238
$880$	−82.7012	−2.78786
$881$	−0.928188	−0.0312714	−0.0156357	−	0.999878i	$-0.504977\pi$
$881$	−0.928188	−0.0312714	−0.0156357	+	0.999878i	$0.504977\pi$
$882$	−9.68287	−0.326039
$883$	33.4131	1.12444	0.562220	−	0.826987i	$-0.309947\pi$
$883$	33.4131	1.12444	0.562220	+	0.826987i	$0.309947\pi$
$884$	1.51732	0.0510331
$885$	119.440	4.01494
$886$	2.54958	0.0856549
$887$	−10.6343	−0.357064	−0.178532	−	0.983934i	$-0.557135\pi$
$887$	−10.6343	−0.357064	−0.178532	+	0.983934i	$0.557135\pi$
$888$	47.8052	1.60424
$889$	−29.3038	−0.982818
$890$	−83.0078	−2.78243
$891$	−50.2052	−1.68194
$892$	1.42550	0.0477293
$893$	16.9765	0.568096
$894$	16.3269	0.546053
$895$	83.3741	2.78689
$896$	21.8782	0.730898
$897$	1.21729	0.0406441
$898$	−49.5189	−1.65247
$899$	4.70263	0.156841
$900$	−2.73069	−0.0910230
$901$	−16.0132	−0.533478
$902$	72.3507	2.40901
$903$	−25.7766	−0.857792
$904$	−31.8906	−1.06067
$905$	3.16640	0.105255
$906$	30.0623	0.998752
$907$	25.4775	0.845965	0.422983	−	0.906138i	$-0.360983\pi$
$907$	25.4775	0.845965	0.422983	+	0.906138i	$0.360983\pi$
$908$	1.43581	0.0476490
$909$	39.1163	1.29741
$910$	34.4048	1.14051
$911$	−41.8901	−1.38788	−0.693940	−	0.720032i	$-0.744127\pi$
$911$	−41.8901	−1.38788	−0.693940	+	0.720032i	$0.744127\pi$
$912$	−41.7922	−1.38388
$913$	43.5538	1.44142
$914$	30.3139	1.00269
$915$	−77.2006	−2.55217
$916$	1.28524	0.0424654
$917$	−8.19004	−0.270459
$918$	−10.9438	−0.361198
$919$	36.1344	1.19196	0.595982	−	0.802997i	$-0.296763\pi$
$919$	36.1344	1.19196	0.595982	+	0.802997i	$0.296763\pi$
$920$	2.36045	0.0778217
$921$	0.477578	0.0157367
$922$	−11.5593	−0.380684
$923$	−39.4802	−1.29951
$924$	1.83016	0.0602080
$925$	99.3073	3.26520
$926$	−8.32178	−0.273471
$927$	23.7894	0.781347
$928$	2.15389	0.0707047
$929$	8.01312	0.262902	0.131451	−	0.991323i	$-0.458036\pi$
$929$	8.01312	0.262902	0.131451	+	0.991323i	$0.458036\pi$
$930$	−13.4723	−0.441773
$931$	12.7505	0.417879
$932$	1.15443	0.0378147
$933$	52.2797	1.71156
$934$	29.7331	0.972896
$935$	−154.657	−5.05781
$936$	−20.1154	−0.657493
$937$	−0.201533	−0.00658379	−0.00329189	−	0.999995i	$-0.501048\pi$
$937$	−0.201533	−0.00658379	−0.00329189	+	0.999995i	$0.501048\pi$
$938$	−2.83796	−0.0926627
$939$	−12.4274	−0.405552
$940$	1.22784	0.0400477
$941$	−33.8285	−1.10278	−0.551388	−	0.834249i	$-0.685902\pi$
$941$	−33.8285	−1.10278	−0.551388	+	0.834249i	$0.685902\pi$
$942$	31.2611	1.01854
$943$	−1.98581	−0.0646669
$944$	44.6584	1.45351
$945$	9.88354	0.321512
$946$	36.3736	1.18261
$947$	−2.91979	−0.0948805	−0.0474402	−	0.998874i	$-0.515106\pi$
$947$	−2.91979	−0.0948805	−0.0474402	+	0.998874i	$0.515106\pi$
$948$	−2.04720	−0.0664901
$949$	6.77404	0.219895
$950$	−90.2795	−2.92906
$951$	−19.5089	−0.632620
$952$	42.6135	1.38111
$953$	−19.2893	−0.624842	−0.312421	−	0.949944i	$-0.601140\pi$
$953$	−19.2893	−0.624842	−0.312421	+	0.949944i	$0.601140\pi$
$954$	7.83155	0.253556
$955$	52.9353	1.71295
$956$	0.640061	0.0207011
$957$	−57.6724	−1.86428
$958$	−1.71488	−0.0554054
$959$	−11.6167	−0.375122
$960$	−85.0834	−2.74605
$961$	−30.1058	−0.971154
$962$	26.9871	0.870099
$963$	23.6562	0.762312
$964$	1.09006	0.0351085
$965$	26.1241	0.840966
$966$	1.26119	0.0405781
$967$	25.1693	0.809389	0.404694	−	0.914452i	$-0.367378\pi$
$967$	25.1693	0.809389	0.404694	+	0.914452i	$0.367378\pi$
$968$	−38.3259	−1.23184
$969$	−78.1542	−2.51067
$970$	−51.8103	−1.66353
$971$	35.5458	1.14072	0.570359	−	0.821395i	$-0.306804\pi$
$971$	35.5458	1.14072	0.570359	+	0.821395i	$0.306804\pi$
$972$	−1.58248	−0.0507580
$973$	−45.8190	−1.46889
$974$	22.4684	0.719935
$975$	−91.2779	−2.92323
$976$	−28.8651	−0.923948
$977$	41.8744	1.33968	0.669840	−	0.742506i	$-0.266363\pi$
$977$	41.8744	1.33968	0.669840	+	0.742506i	$0.266363\pi$
$978$	−26.8387	−0.858206
$979$	−67.5698	−2.15954
$980$	0.922190	0.0294583
$981$	−16.8939	−0.539381
$982$	3.37733	0.107775
$983$	1.00000	0.0318950
$983$	1.00000	0.0318950
$984$	71.6808	2.28510
$985$	−4.43117	−0.141189
$986$	−49.5385	−1.57763
$987$	17.7832	0.566046
$988$	0.977167	0.0310878
$989$	−0.998348	−0.0317456
$990$	75.6375	2.40392
$991$	11.5576	0.367139	0.183569	−	0.983007i	$-0.441235\pi$
$991$	11.5576	0.367139	0.183569	+	0.983007i	$0.441235\pi$
$992$	0.409571	0.0130039
$993$	45.4565	1.44252
$994$	−40.9040	−1.29740
$995$	54.8991	1.74042
$996$	1.59186	0.0504400
$997$	28.9379	0.916473	0.458236	−	0.888830i	$-0.348481\pi$
$997$	28.9379	0.916473	0.458236	+	0.888830i	$0.348481\pi$
$998$	28.6619	0.907277
$999$	7.75264	0.245283

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.2.a.b.1.38	✓	54
3.2	odd	2		8847.2.a.g.1.17		54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.2.a.b.1.38	✓	54	1.1	even	1	trivial
8847.2.a.g.1.17		54	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 983 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	983.a (trivial)

\(f(q)\)	\(=\)	\(q+1.38686 q^{2} -2.35222 q^{3} -0.0766077 q^{4} +4.36721 q^{5} -3.26221 q^{6} +2.06000 q^{7} -2.87997 q^{8} +2.53295 q^{9} +O(q^{10})\)	\(q+1.38686 q^{2} -2.35222 q^{3} -0.0766077 q^{4} +4.36721 q^{5} -3.26221 q^{6} +2.06000 q^{7} -2.87997 q^{8} +2.53295 q^{9} +6.05673 q^{10} +4.93029 q^{11} +0.180198 q^{12} +2.75749 q^{13} +2.85694 q^{14} -10.2727 q^{15} -3.84092 q^{16} -7.18276 q^{17} +3.51286 q^{18} -4.62575 q^{19} -0.334562 q^{20} -4.84557 q^{21} +6.83764 q^{22} -0.187673 q^{23} +6.77434 q^{24} +14.0726 q^{25} +3.82427 q^{26} +1.09860 q^{27} -0.157812 q^{28} +4.97299 q^{29} -14.2468 q^{30} +0.945635 q^{31} +0.433117 q^{32} -11.5971 q^{33} -9.96152 q^{34} +8.99645 q^{35} -0.194044 q^{36} +7.05680 q^{37} -6.41529 q^{38} -6.48623 q^{39} -12.5775 q^{40} +10.5812 q^{41} -6.72015 q^{42} +5.31962 q^{43} -0.377698 q^{44} +11.0619 q^{45} -0.260277 q^{46} -3.66999 q^{47} +9.03469 q^{48} -2.75641 q^{49} +19.5167 q^{50} +16.8955 q^{51} -0.211245 q^{52} +2.22940 q^{53} +1.52362 q^{54} +21.5316 q^{55} -5.93274 q^{56} +10.8808 q^{57} +6.89686 q^{58} -11.6270 q^{59} +0.786965 q^{60} +7.51515 q^{61} +1.31147 q^{62} +5.21787 q^{63} +8.28251 q^{64} +12.0426 q^{65} -16.0837 q^{66} -0.993358 q^{67} +0.550255 q^{68} +0.441448 q^{69} +12.4769 q^{70} -14.3174 q^{71} -7.29483 q^{72} +2.45659 q^{73} +9.78683 q^{74} -33.1018 q^{75} +0.354368 q^{76} +10.1564 q^{77} -8.99552 q^{78} -11.3608 q^{79} -16.7741 q^{80} -10.1830 q^{81} +14.6747 q^{82} +8.83392 q^{83} +0.371208 q^{84} -31.3687 q^{85} +7.37759 q^{86} -11.6976 q^{87} -14.1991 q^{88} -13.7050 q^{89} +15.3414 q^{90} +5.68043 q^{91} +0.0143772 q^{92} -2.22434 q^{93} -5.08978 q^{94} -20.2016 q^{95} -1.01879 q^{96} -8.55417 q^{97} -3.82276 q^{98} +12.4882 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 8 q^{2} + 6 q^{3} + 64 q^{4} + 7 q^{5} + 5 q^{6} + 31 q^{7} + 24 q^{8} + 74 q^{9}+O(q^{10}) \) 54 * q + 8 * q^2 + 6 * q^3 + 64 * q^4 + 7 * q^5 + 5 * q^6 + 31 * q^7 + 24 * q^8 + 74 * q^9	\( 54 q + 8 q^{2} + 6 q^{3} + 64 q^{4} + 7 q^{5} + 5 q^{6} + 31 q^{7} + 24 q^{8} + 74 q^{9} + 15 q^{10} + 8 q^{11} + 10 q^{12} + 34 q^{13} + q^{14} + 3 q^{15} + 80 q^{16} + 32 q^{17} + 28 q^{18} + 15 q^{19} + 4 q^{20} + 11 q^{21} + 25 q^{22} + 15 q^{23} - 7 q^{24} + 125 q^{25} - 14 q^{26} + 12 q^{27} + 78 q^{28} + 8 q^{29} - 32 q^{30} + 16 q^{31} + 36 q^{32} + 38 q^{33} - 8 q^{34} - 2 q^{35} + 65 q^{36} + 80 q^{37} - 14 q^{38} + 16 q^{39} + 36 q^{40} + 30 q^{41} - 10 q^{42} + 53 q^{43} + 6 q^{44} + 3 q^{45} + 24 q^{46} + 22 q^{47} + 7 q^{48} + 111 q^{49} + 14 q^{50} - 10 q^{51} + 45 q^{52} + 10 q^{53} - 8 q^{54} + 12 q^{55} - 30 q^{56} + 106 q^{57} + 61 q^{58} - 4 q^{59} - 61 q^{60} + 24 q^{61} - 12 q^{62} + 73 q^{63} + 86 q^{64} + 32 q^{65} - 43 q^{66} + 54 q^{67} + 33 q^{68} - 30 q^{69} - 21 q^{70} - 6 q^{71} + 60 q^{72} + 172 q^{73} - 32 q^{74} - 36 q^{75} + 7 q^{76} - 12 q^{77} - 3 q^{78} + 28 q^{79} - 66 q^{80} + 86 q^{81} + 4 q^{82} + 14 q^{83} - 58 q^{84} + 99 q^{85} - 31 q^{86} - 27 q^{87} + 5 q^{88} - 5 q^{89} - 45 q^{90} - 11 q^{91} + 20 q^{92} + 27 q^{93} - 39 q^{94} + 5 q^{95} - 87 q^{96} + 127 q^{97} - 29 q^{98} - 21 q^{99}+O(q^{100}) \) 54 * q + 8 * q^2 + 6 * q^3 + 64 * q^4 + 7 * q^5 + 5 * q^6 + 31 * q^7 + 24 * q^8 + 74 * q^9 + 15 * q^10 + 8 * q^11 + 10 * q^12 + 34 * q^13 + q^14 + 3 * q^15 + 80 * q^16 + 32 * q^17 + 28 * q^18 + 15 * q^19 + 4 * q^20 + 11 * q^21 + 25 * q^22 + 15 * q^23 - 7 * q^24 + 125 * q^25 - 14 * q^26 + 12 * q^27 + 78 * q^28 + 8 * q^29 - 32 * q^30 + 16 * q^31 + 36 * q^32 + 38 * q^33 - 8 * q^34 - 2 * q^35 + 65 * q^36 + 80 * q^37 - 14 * q^38 + 16 * q^39 + 36 * q^40 + 30 * q^41 - 10 * q^42 + 53 * q^43 + 6 * q^44 + 3 * q^45 + 24 * q^46 + 22 * q^47 + 7 * q^48 + 111 * q^49 + 14 * q^50 - 10 * q^51 + 45 * q^52 + 10 * q^53 - 8 * q^54 + 12 * q^55 - 30 * q^56 + 106 * q^57 + 61 * q^58 - 4 * q^59 - 61 * q^60 + 24 * q^61 - 12 * q^62 + 73 * q^63 + 86 * q^64 + 32 * q^65 - 43 * q^66 + 54 * q^67 + 33 * q^68 - 30 * q^69 - 21 * q^70 - 6 * q^71 + 60 * q^72 + 172 * q^73 - 32 * q^74 - 36 * q^75 + 7 * q^76 - 12 * q^77 - 3 * q^78 + 28 * q^79 - 66 * q^80 + 86 * q^81 + 4 * q^82 + 14 * q^83 - 58 * q^84 + 99 * q^85 - 31 * q^86 - 27 * q^87 + 5 * q^88 - 5 * q^89 - 45 * q^90 - 11 * q^91 + 20 * q^92 + 27 * q^93 - 39 * q^94 + 5 * q^95 - 87 * q^96 + 127 * q^97 - 29 * q^98 - 21 * q^99

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